Concentration Terms of Solutions

Most chemical reactions studied in the laboratory take place between substances dissolved in a solvent, not

between pure solids or gases — so chemists need precise, standardised ways of stating how much solute is

present in a given solution. A solution is made of a solute (the substance being dissolved, usually the

smaller quantity) dissolved in a solvent (usually the larger quantity, most commonly water). Several

different "concentration terms" are in everyday use, each suited to a different kind of calculation.

Molarity ($M$). Molarity is the number of moles of solute dissolved per litre of solution (not per litre

of solvent):

Molarity is the most widely used concentration term in the laboratory because volumes of solution are easy to

measure with burettes, pipettes and volumetric flasks. Its one drawback is that it changes slightly with

temperature, because the volume of a liquid expands or contracts as temperature changes, even though the

number of moles of solute stays fixed.

Molality ($m$). Molality is the number of moles of solute dissolved per kilogram of solvent (not

solution):

Because molality is defined using the mass of the solvent rather than the volume of the solution, it does

not change with temperature — this makes it the preferred concentration term for precise physical-chemistry

work (such as measuring boiling-point elevation or freezing-point depression).

Normality ($N$). Normality is the number of gram equivalents of solute dissolved per litre of solution:

The number of gram equivalents is obtained by multiplying the number of moles of solute by its "$n$-factor" —

for an acid, the $n$-factor is the number of replaceable $\text{H}^+$ ions per molecule (so for

$\text{H}_2\text{SO}_4$, $n\text{-factor} = 2$); for a base, it is the number of replaceable $\text{OH}^-$ ions.

Normality is therefore always a whole-number multiple of molarity: $N = n\text{-factor} \times M$.

Mole fraction ($x$). Mole fraction expresses concentration as a pure ratio of moles, with no reference to

mass or volume at all — it is the number of moles of one component divided by the total number of moles of

all components present in the solution:

Mole fractions have no unit, and the mole fractions of all components of a solution must always add up to

exactly $1$. Mole fraction is especially useful in the study of gas mixtures and in relating vapour pressure to

composition (Raoult's law).

Percentage concentration. Two common percentage-based terms are mass percentage (mass of solute divided by …